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Here we study the statistical properties of two-dimensional spin ice in itsground state by the Monte Carlo simulation method. Using a new samplingalgorithm, we show that the short-range ice rule in two dimensions gives riseto long-range but not dipole-like correlations, to non-Gaussian probabilitydensity function for magnetization and to non-extensive conditional entropy(entropy with given value of magnetization).

Do dipole correlations exist in two-dimensional spin ice?